WASHINGTON >> Census Bureau experts have uncovered serious flaws in a section of the 2020 head count that potentially affect the enumeration of millions, according to people familiar with the census operations, delaying still further the completion of state-by-state population totals that the White House has demanded before President Donald Trump leaves office next month.

Census experts told the Trump administration last month that data-processing delays were making it impossible to meet that schedule, but the agency’s political appointees have continued to press for shortcuts in an attempt to deliver on the White House’s demand. On Friday, people involved with the census but not authorized to make official comments said the latest delay — adding 10 to 14 more days to a process that was already set to end well beyond the Dec. 31 statutory deadline — appeared to doom that last-ditch rush.

The extent of the additional problems — relating to the count of residents of group quarters like prisons, college dormitories or homeless shelters — effectively means that “that isn’t going to happen,” one official, who declined to be named for fear of retribution, said of meeting the deadline.

The Trump administration needs the bureau’s state-by-state population totals if it is to fulfill the president’s plan to strip immigrants without legal status from the state counts used to reapportion the House of Representatives. Such a move, unprecedented in American history, would produce an older, whiter, more rural population base for reallocating House seats that would mostly benefit Republicans, analysts say.

Many experts see the bureau facing deadlines it cannot possibly meet while maintaining its standards. Some bureau officials remain concerned that Trump will demand numbers anyway, a move that could plunge the nation into uncharted legal territory if the Democratic House and the new Biden administration reject the results.

The week’s developments are but the latest trials in a beleaguered and fraught census, with career officials forced to steer between a pandemic that all but halted the count for months and political pressure from the White House for results on the president’s timetable — sometimes, some career experts say, with little regard for accuracy.

“Anything produced in this compressed timeline the Trump administration has set increases the chances of a corrupted census,” Vanita Gupta, the president of the Leadership Conference on Civil and Human Rights, said Friday. “The data problems can be fixed and the deadlines extended. But career census experts need to be able to fix the problems before the count is submitted. If the final data that is sent is shoddy, that could mean a failed census altogether.”

Spokespeople for the Commerce Department and the Census Bureau did not immediately respond to requests for comment.

Trump’s July order put enormous stress on the Census Bureau and its system for processing data at a time when it was also contending with the challenge of the pandemic.

With counting operations all but ground to a halt in the spring, the administration asked Congress in April to extend the legal deadline for delivering reapportionment totals to April 2021, rather than Dec. 31.

But in July, Trump abruptly reversed course, ordering that the Dec. 31 deadline be met. That forced Census Bureau experts to compress five months of data processing into two and a half months.

The Supreme Court heard arguments this week in two lawsuits contending that Trump’s plan violated federal law and the Constitution, which says the census should count all residents, not just citizens, and requires congressional districts to be apportioned “counting the whole number of persons in each state,” using information from the census.

The latest problems, which were not discussed at the Supreme Court argument, involve the tabulation of a category — people who live in group quarters — which totaled about 7.5 million residents in 2010, according to that year’s census.

To provide accurate numbers, the census asks for advance estimates from the institutions that house many people and then matches those estimates with the totals it receives from census-takers in the field. This month, data processing operations have turned up large discrepancies between the two numbers in group quarters nationwide, differences that can probably be resolved only by further review and in some cases returning to the field. (For example, a homeless shelter or a prison might have expected to house a larger number of daily residents than it actually had when the census was conducted.)

By itself, that is not unusual; the bureau found similar variances in censuses in 2010 and 2000. In 2013, the bureau described how the numbers for residents of group quarters were resolved in a chart that is part of the 2010 census Planning Memoranda Series — effectively reducing the process to a historical footnote.

But in those previous decennial counts, time had been built into the data-processing schedule to remedy that and other problems. This year, in its rush to produce figures for the White House, the Census Bureau had already cut its data-processing schedule nearly in half, leaving no margin for mistakes.

Moreover, the discrepancies are exceptionally large this time because the coronavirus pandemic disrupted census work and led many residents of group quarters to move in the middle of the head count. This category includes college students in dormitories or off-campus apartments, many of whom returned home when the pandemic forced an end to in-person classes.

In meetings this week, the bureau ordered teams to find the source of the problems and recommend fixes by Sunday.

Problems counting university students appear to have been worsened by requirements of federal privacy laws that Congress failed to address before the count began. At least one university omitted last names of its dormitory residents in files sent to the bureau. Many schools did not turn over addresses of students who lived off campus but returned home, meaning that census-takers in college towns had no idea whether vacant apartments they found were truly empty or should be counted as a student’s place of residence.

Multiply that by millions of people who moved during the pandemic — children who brought parents home from nursing homes, jobless children who moved in with parents, relatives who consolidated households when money ran short — and the scope of the bureau’s problems becomes apparent, said Ron Santos, the vice president of the Urban Institute and president-elect of the American Statistical Association.

“They could be in a situation where they don’t know what they don’t know, and by the time they find out, it’s too late,” Santos said. “I don’t have high confidence that this can be done in two weeks, or three weeks, or a month. I think the Census Bureau needs time to do its due diligence, sort out the problems and fix them.”